Drummer Jeff Cosgrove isn’t that well known yet, but he’s built an impressive catalog of recordings over the last decade. His first album as a leader, 2011’s For the Love of Sarah, was a collection of pieces by drummer Paul Motian, released under the name Motian Sickness; it featured Mat Maneri on viola, John Hébert on bass, and Jamie Masefield on mandolin. He’s also made several recordings with pianist Matthew Shipp and bassist William Parker, and one with Shipp and saxophonist Ivo Perelman.

On his latest album, History Gets Ahead of the Story, he adapts the music of Parker’s long-running quartet (with trumpeter Lewis “Flip” Barnes, alto saxophonist Rob Brown, and drummer Hamid Drake) for an organ trio that features saxophonist Jeff Lederer and organist John Medeski. Seven of the ten compositions are Parker’s; Cosgrove contributes one, and Lederer two.

The music of the William Parker Quartet — which frequently transformed into Raining On The Moon with the addition of vocalist Leena Conquest — is some of the most mainstream-friendly in the bassist’s catalog. The tunes have punchy, bluesy heads, solos are exploratory but rarely harsh or screechy, and Parker and Drake lock into throbbing grooves that allow pieces like “Corn Meal Dance” or “Wood Flute Song” to stretch toward, and even pass, the 10-minute mark while remaining foot-tapping at all times. It’s a cross between hard bop and trance music that really comes alive onstage, though the band’s studio albums, O’Neal’s Porch and Petit Oiseau, are fantastically vital and joyous.

What’s interesting about History Gets Ahead of the Story is how different this music sounds in other players’ hands. One might expect an organ trio to take these hard-driving pieces in an even more soul-jazz direction, but that’s not always the case. On the album-closing “Harlem,” they dig deep into the blues, but there’s plenty of free-form exploration here, too. Cosgrove is a much less locked-in drummer than Drake; though he keeps the groove tight when the mood calls for it, his playing has a shifting abstraction more reminiscent of Milford Graves. Medeski’s organ playing is closer to the spaciness of Larry Young than to heavy Blue Note artists like Big John Patton or Baby Face Willette. Lederer has always felt free to go as far out as the moment demands; his 2011 album Sunwatcher was a tribute to Albert Ayler that featured plenty of fierce, prayerful lines, and some of that same outward-bound exultation is heard here. But what’s really surprising is the concision the trio displays. The longest track here is the opening “O’Neal’s Porch,” at 6:55; the shortest is the abstract “Things Fall Apart,” which runs a mere 4:29. Cosgrove and company aren’t interested in settling into the endless trance grooves the quartet specialized in; they’re treating these pieces as songs, and shining a bright light on William Parker the composer in the process.

—Phil Freeman